There are eighty women and sixty men in the class. Thirty women and thirty men own dogs. The lecturer shuts his or her eyes, spins around, and points to a person at random.

a. What is the probability that the person picked:

i. Is a woman?

ii. Owns a dog?

iii. Is a female dog owner?

iv. Is either a woman or a dog owner?

b. Relate your answer in part a to the formula P(E U F) = P(E) + P(F) - P(E n F).

c. In this situation are the events "being a woman" and "being a dog owner"

independent, mutually exclusive, or neither? POLI967